the Rotatory Motion of Bodies,. 331 
I do not £ nd that the refolving the forces H, I, K, in any other 
fmnner will conduce to the attainment of any ufeful conclufion. 
It appears, by what is done above, that the force 
H is = x CD Wft 
3 a 3 RT 
I is = X BC . C«“ - B/s* . y’y, 
3« 3r T 
K = ^4- X BDV; ! S’S ; 
3<2 3 RT 
R being = By F 4-D 2 /3T+C 2 /3y. 
And it is obvious, that each of the three lafi mentioned forces 
will be = o, if any two of the quantities b, c, d, be equal; 
two of the values of* tliofe forces then vanifhing, by reafon of 
that equality ; and the third value alfo vanishing by either 
/§, y, or being at the fame time — o. Therefore, in that 
cafe it . happens, that M. Euler’s computation agrees with 
mine: in every other cafe, I am clearly of opinion, his con- 
-clufions are not true. The fame may be faid of M. D’Alem- 
bert’s conclusions refpecting the fame propolition. 
The. evagation of the pole of a revolving body confidered 
above, does not arife from gravity, the attraction of any other 
body, or any external impulfe whatever ; but is only the con - 1 - 
fequence of the inertia of matter , and mult neceflarily enfue 3 
according to the theory here explained, in every body in the 
univerfe, after having been made to revolve, without reflraint, 
about any line paffing through its center of gravity, that is not a 
permanent axis of rotation. 
The Earth being neither uniformly denfe nor a perfect 
fpheroid muft, in ftridtnefs, be confidered as having only three 
permanent axes of rotation, agreeably , to what T have proved 
in my Mathematical Memoirs', and,-. as it is difturbed in its 
rotatory motion by the attraction of the fun and moon (and 
other 
